Shirley Sears Chater breezed through her confirmation hearing to head the troubled Social Security Administration, telling a Senate committee that “a distinct and disturbing lack of public confidence” in the system must be overcome. The failure of President Clinton’s nominee to pay Social Security taxes for a part-time baby-sitter in the early 1970s was barely mentioned. Chater, 61, president of Texas Women’s University, said in the letter she and her husband paid the taxes last July that should have been paid for a part-time baby-sitter between 1969 and 1975.